7.22 Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium:
2BrCl (g) Br2 (g) + Cl2 (g)
for which Kc= 32 at 500 K. If initially pure BrCl is present at a concentration of
3.3 × 10–3 mol L–1, what is its molar concentration in the mixture at equilibrium?
Let the amount of bromine and chlorine formed at equilibrium be x. The given reaction is:
2BrCl(g) ↔ Br2(g) + Cl2(g)
Initial conc. 3.3×10-3 0 0
At equilibrium 3.3×10-3 -2x x x
Now, we can write,
[Br2][Cl2][BrCl]2=Kc
⇒x×x(3.3×10-3-2x)2=32
⇒x=18.678×10-3-11.32x
⇒12.32x=18.678×10-3
⇒x=1.5×10-3
Therefore, at equilibrium,
[BrCl]=3.3×10-3-(2×1.5×10-3)
=3.3×10-3-3.0×10-3
=0.3×10-3
=3.0×10-4 molL-1
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